Best Known (6−4, 6, s)-Nets in Base 9
(6−4, 6, 36)-Net over F9 — Constructive and digital
Digital (2, 6, 36)-net over F9, using
- net defined by OOA [i] based on linear OOA(96, 36, F9, 4, 4) (dual of [(36, 4), 138, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(96, 36, F9, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- appending kth column [i] based on linear OOA(96, 36, F9, 3, 4) (dual of [(36, 3), 102, 5]-NRT-code), using
(6−4, 6, 43)-Net over F9 — Digital
Digital (2, 6, 43)-net over F9, using
- net defined by OOA [i] based on linear OOA(96, 43, F9, 4, 4) (dual of [(43, 4), 166, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(96, 43, F9, 3, 4) (dual of [(43, 3), 123, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(96, 43, F9, 4) (dual of [43, 37, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(96, 43, F9, 4) (dual of [43, 37, 5]-code), using
- appending kth column [i] based on linear OOA(96, 43, F9, 3, 4) (dual of [(43, 3), 123, 5]-NRT-code), using
(6−4, 6, 128)-Net in Base 9 — Upper bound on s
There is no (2, 6, 129)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 538705 > 96 [i]
- extracting embedded orthogonal array [i] would yield OA(96, 129, S9, 4), but
- the linear programming bound shows that M ≥ 10240 704045 / 19093 > 96 [i]